Despite intense research efforts that have provided enormous insight, cancer continues to be a poorly understood disease. There has been much debate over whether the cancerous state can be said to originate in a single cell or whether it is a reflection of aberrant behaviour on the part of a 'society of cells'. This article presents, in the form of a debate conducted among the authors, three views of how the problem might be addressed. We do not claim that the views exhaust all possibilities. These views are (a) the tissue organization field theory (TOFT) that is based on a breakdown of tissue organization involving many cells from different embryological layers, (b) the cancer stem cell (CSC) hypothesis that focuses on genetic and epigenetic changes that take place within single cells, and (c) the proposition that rewiring of the cell's protein interaction networks mediated by intrinsically disordered proteins (IDPs) drives the tumorigenic process. The views are based on different philosophical approaches. In detail, they differ on some points and agree on others. It is left to the reader to decide whether one approach to understanding cancer appears more promising than the other.